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MacbethInitially, Macbeth is incredulous; he cannot believe what the Weird Sisters have told him. He wants them to keep talking and to tell him more, including how they know the information they claim to...

MathHello! I suppose that the age of each child is a natural (whole) number. Then from (b) we get that Alejandra's age is a natural number greater than 8 but less than 10. There is the only such...

LiteratureIn the story, Okonkwo is Ezekiel's brother; after Ezekiel's death, he takes Ezekiel's widow, Ma Blackie, as his fourth wife. Even in postcolonial Nigeria, the traditions are such that a woman's...

The Bronze BowThroughout The Bronze Bow, Samson and Leah have several similarities. Both individuals are loyal, innocent, and talented. Samson not only obeys Daniel, but also helps and protects him throughout...

The GiverThe community that Jonas lives in with his family has many rules. The purpose of these rules is to maintain order and particular standards. The people in the community are controlled by the many...

Law and PoliticsThomas Jefferson wrote the Declaration of Independence. In the Declaration of Independence, there are many ideas about the role of government and about the rights the people should have. A big part...

The Yellow Wallpaper"The Yellow Wallpaper" by Charlotte Perkins Gilman is not an example of crime fiction or a crime story. First, one should note that crime fiction is a genre defined by far more than the simple...

Declaration of IndependenceIn the Declaration of Independence, Thomas Jefferson argues that the King of England does not have any respect for the laws of the colonies and does not care about the rights that those laws are...

ScienceI will start with the independent variable. The independent variable in an experiment is the variable the experimenter has control over. For example, if you are testing the effect of amounts of...

The Fall of the House of UsherDuring the tempestuous storm in the final moments of "The Fall of the House of Usher," Roderick Usher reveals a very disturbing fact to the narrator. Early in the story, the two men buried the...

The Human ComedyAdults treat children very respectfully and as equals in The Human Comedy. For example, in Chapter 3, Mr. Spangler, Homer's boss at the telegraph office, asks Homer how he likes working at the...

Romeo and JulietIn many ways, it could be said that Juliet's hotheaded cousin Tybalt is responsible for Romeo and Juliet's deaths. In Act III, Scene 1, Tybalt challenges Romeo to a duel. Romeo refuses, but...

RikkiTikkiTaviRikkiTikkiTavi does a number of good things in the story. As the main protagonist, RikkiTikkiTavi proves himself to be an altruistic hero. For example, after he is rescued by the family,...

The Legend of Sleepy HollowIchabod Crane is considered an important person in Sleepy Hollow. This idea might seem strange, as Ichabod is undoubtedly ridiculous and comical by turns, but the fact remains that he's a school...

Death, be not proud"Death, be not proud" is a sonnet by the iconic English metaphysical poet John Donne. The fourteenline poem, which is also referred to as "Holy Sonnet X,"deals with the fear of death, overcoming...

The CrucibleThe debut of The Crucible at the Martin Beck Theater on Broadway in January of 1953 was met with rather lukewarm reviews, though it did receive the Tony award for best play. Brooks Atkinson wrote...

The NecklaceDespite the turn in her fortunes, Mathilde still dreams of a life of ease and wealth. She remembers how admired she was at the ball years ago, and still yearns for the adoration and regard of...

RikkiTikkiTaviThe story "RikkiTikkiTavi" contains the word "veranda" a total of eight times. The usage of the word is not special or unique in the story, though. Kipling uses the word according to a standard...

RikkiTikkiTaviIn the story, "RikkiTikkiTavi," Rikki Tikki destroys Nag and Nagaina's eggs, even though he was...The answer to this really depends on your own personal opinion. On the one hand, you can argue that Rikki Tikki is hypocritical in the story "RikkiTikkiTavi." On the other, you can argue that...

Number the StarsLois Lowry's work of historical fiction, Number the Stars, follows the story of Annemarie Johansen, who puts her life at stake to rescue her Jewish best friend, Ellen Rosen, from being sent to a...

The LotteryIn "The Lottery," the draw takes place on a summer day and every member of the town  approximately three hundred people  must take part. Assembled in the square in which all civic events take...

Raymond's RunWhen examining the text, it becomes apparent that Raymond plays a pivotal role in Tony Cade Bambara’s short story “Raymond’s Run.” Although Hazel Elizabeth Deborah Parker, known as Squeaky,...

To Kill a MockingbirdIn Chapter 3, Scout watches as Walter Cunningham Jr. pours syrup all over his meat and vegetables. Scout is disgusted and asks Walter what the "sam hill" he is doing. Atticus quickly glances at his...

Everyday UseIn the story, both Maggie and Dee desired two family heirloom quilts for themselves, but they have very different reasons for wanting them. The quilts contained pieces of clothing worn by relatives...

HamletYour question apparently refers to the exchange between Hamlet and his mother in Act III, Scene 4, right after Hamlet kills Polonius, who was hiding behind the arras. Gertrude is horrified. She...

RikkiTikkiTaviA family might want a mongoose as a pet for the same reasons that a family might want a dog or a cat for a pet. A mongoose is soft and cute looking (in my opinion). A more objective reason to...

HootThere are several possible reasons why Roy, the main character in Carl Hiaasen's novel Hoot, is interested in the running boy. One of the main reasons is that Roy's interest in the running boy is...

GrammarThe primary reason this sentence is ambiguous is because of the unclear placement and use of the word "right." In the English language, the word "right" can mean two very different things. The...

The Witch of Blackbird PondIn The Witch of Blackbird Pond, Hannah Tupper is forced to live a life of tremendous isolation, with her cottage located at the edge of the swamp on the outskirts of town. The people of...

Animal FarmIn Animal Farm, there is an external conflict between animals and humans. Orwell introduces this conflict early in the story: in Chapter One, for example, Old Major expresses this conflict when he...

Reference'Ambiguity' means a lack of clarity or concrete detail, which can make it difficult to discern meaning. In the case of these two sentences, the lack of context and detail make it possible to...

MathGiven `dy/dx = 1/sqrt(4x^2) ` and `y(0) = pi` We have to find y. So we can write, `dy=dx/sqrt(4x^2)` Integrating both sides we have, `y=int dx/sqrt{4x^2)+C` Now let `x=2sint ` So, `dx=2cost...

MathRecall that` int f(x) dx = F(x) +C` where: f(x) as the integrand function F(x) as the antiderivative of f(x) C as the constant of integration.. For the given problem, the integral: `int...

MathComplete the square at the denominator: `x^4 + 2x^2 + 2 = (x^2)^2 + 2x^2 + 1 + 1 = (x^2 + 1)^2 + 1.` Now we see the substitution `y = x^2 + 1,` then `dy = 2x dx,` and the integral becomes `int...

MathWe have to evaluate the integral: `\int \frac{1}{(x1)\sqrt{x^22x}}dx` We can write the integral as: `\int \frac{1}{(x1)\sqrt{x^22x}}dx=\int \frac{1}{(x1)\sqrt{(x1)^21}}dx` Let `x1=t` So...

MathRecall that `int_a^b f(x) dx = F(x)_a^b` : `f(x)` as the integrand function `F(x) ` as the antiderivative of `f(x)` "a" as the lower boundary value of x "b" as the upper boundary value of x To...

MathTo evaluate the given integral:` int 2/sqrt(x^2+4x)dx` , we may apply the basic integration property: `int c*f(x)dx= c int f(x)dx` . The integral becomes: `2 int dx/sqrt(x^2+4x)` We complete the...

MathBy completing the square and making simple substitution, we will reduce this integral to a table one. `x^24x = (x^2 + 4x + 4) + 4 = (x+2)^2 + 4 = 4  (x+2)^2.` Now make a substitution `y =...

MathWe have to evaluate the integral:`` `\int \frac{2x5}{x^2+2x+2}dx` We can write the integral as: `\int \frac{2x5}{x^2+2x+2}dx=\int\frac{2x5}{(x+1)^2+1}dx` Let `x+1=t` So, `dx=dt` Now we can write...

MathFor the given integral: `int 2x/(x^2+6x+13) dx` , we may apply the basic integration property: `int c*f(x) dx = c int f(x) dx` . `int 2x/(x^2+6x+13) dx =2 int x/(x^2+6x+13) dx` To be able to...

MathTo evaluate the given integral: `int_(2)^(2)(dx)/(x^2+4x+13)` , we follow the first fundamental theorem of calculus: If f is continuous on closed interval [a,b], we follow: ` int_a^bf(x)dx =...

MathTo be able to evaluate the given integral:` int_0^2 (dx)/(x^22x+2)` , we complete the square of the expression:`x^22x+2` . To complete the square, we add and subtract `(b/(2a))^2` . The...

MathRecall that `(arccos(x))' = 1/sqrt(1x^2)` and make the substitution `y = arccos(x),` then `dy = 1/sqrt(1x^2).` The limits of integration are from `arccos(0) = pi/2` to `arccos(1/sqrt(2)) =...

MathWe have to evaluate the definite integral: `\int_{0}^{1/\sqrt{2}}\frac{arc sinx}{\sqrt{1x^2}}dx` Let `t= arcsinx` Differentiating both sides we get, `\frac{1}{\sqrt{1x^2}}dx=dt`...

MathMake the substitution `u = sin(x),` then `du = cos(x) dx.` The integration limits for `u` are from `sin(0) = 0` to `sin(pi/2) = 1,` and the integral becomes `int_0^1 (du)/(1 + u^2) = arctan(1) ...

MathWe have to evaluate the integral: `\int_{\pi/2}^{\pi}\frac{sinx}{1+cos^2x}dx` Let `cosx=u` So, `sinx dx=du` When `x=\pi/2, u=0` `x=\pi, u=1` So we have,...

MathMake the substitution `y = e^(x),` then `dy = e^(x) dx` and `e^(2x) = y^2.` The limits of integrations for `y` become from `e^(ln2) = 1/e^(ln2) = 1/2` to `e^(ln4) = 1/e^(ln4) = 1/4.` The...

MathFor the given integral problem:` int_0^(ln(5))e^x/(1+e^(2x))dx` , it resembles the basic integration formula for inverse tangent: `int_a^b (du)/(u^2+c^2) = (1/c)arctan(u/c) _a^b` where we let:...

MathMake the substitution `u = sqrt(16x^2  5),` then `16x^2 = u^2 + 5,` `du = (32x)/(2sqrt(16x^2  5)) dx = (16 x dx)/sqrt(16x^2  5),` or `dx/sqrt(16x^2  5) = (du)/(16 x).` The limits of...

MathTo be able to solve for definite integral, we follow the first fundamental theorem of calculus: `int_a^b f(x) dx = F(x) +C` such that f is continuous and F is the antiderivative of f in a closed...